Name
ID
MATH 172
EXAM 1
Section 504
Spring 1999
1-10
/60
11
/10
12
/10
13
/10
14
/10
P. Yasskin
Multiple Choice: (6 points each)
3
; 2 9 " x 2 dx
1. Evaluate
a. 6 9=
by interpretating it as an area.
0
4
b. 3 9=
c. 2 9=
2
d. 2 9=
e. 6 9=
2. Compute:
;
2
1
a. 47
b.
c.
d.
e.
x 3 x 13
x
dx
8
45
8
351
64
415
64
417
64
3. Compute:
;
=/4
0
cos 3 2 sin 2 d2
a. " 3
b.
c.
d.
e.
16
" 1
16
1
16
3
16
3
1
2
d ; x e t 2 dt
dx x
4. Compute:
a.
b.
c.
d.
e.
ex " ex
4
2
e x 2x " e x
4
2
e x 4x 3 " e x
2
2
e 4x " e x
2
2
e 4x 2x " e x
4
5. Compute:
a.
b.
c.
d.
e.
b.
c.
d.
e.
x 2 1 dx
2
3
Ÿx 3x ;
"3 C
x 3 3x
"1 C
x 3 3x
"1
C
3
3x 9x
1
C
x 3 3x
3
C
x 3 3x
e
; x 4 lnx dx
1
4 e5 1
25
25
4 e5 " 1
25
25
4 Ÿe 5 " 1 25
4 Ÿe 5 1 25
1 Ÿe 5 1 5
6. Compute:
a.
2
2
7. Find the area between the curves
a. 2
b. 4
c. 12
d. 24
e. 32
y 12 " x 2
and
y y 2x 2 .
1
8.
The region below
0txt
for
=
y sinŸx
2
above the x-axis
is rotated about the y-axis.
Find the volume of the solid swept out.
-2
-1
0
1
x
2
a. =
b.
c.
d.
e.
2
=
2=
3=
4=
3
9. The force needed to stretch a superspring
beyond its natural length is
xm
how much
If it takes
to stretch the superspring by
32 N
2 m,
F kx
to
work is done in stretching it from
2m?
1m
a. 3
b. 7
c. 15
d. 31
e. 63
3.
10. The mass density of a 9 m rod is > average density of the rod.
kg
a. .495 m
kg
18
3 m
1
x
Ÿ
for 0 t x t 9. Find the
kg
b. .99 m
kg
c. .4995 m
kg
d. .999 m
kg
e. .49995 m
4
11. (10 points)
Compute:
1
; arctan2x dx
0 1x
12. (10 points)
Compute:
; sec 3 2 tan 3 2 d2
5
13.
(10 points)
A hemispherical bowl of radius
is filled to a depth of
2 ft
1 ft.
Find the volume of the water.
HINT: Slice it horizontally.
14. (10 points)
How much work is done in pumping the water out the top of the bowl
shown in problem 13? Leave the density as > and the acceleration of gravity as g.
6